Differential operators and immersions of a Riemann surface into a Grassmannian

Biswas, Indranil (2002) Differential operators and immersions of a Riemann surface into a Grassmannian Journal of Geometry and Physics, 41 (4). pp. 286-295. ISSN 0393-0440

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Official URL: http://linkinghub.elsevier.com/retrieve/pii/S03930...

Related URL: http://dx.doi.org/10.1016/S0393-0440(01)00062-6

Abstract

We consider equivariant holomorphic immersions of a universal cover X of a compact Riemann surface X into a Grassmannian G(n,C2n) satisfying a nondegeneracy condition. The equivariance condition says that there is a homomorphism ρ of the Galois group to GL(2n,C) that takes the natural action of the Galois group on X to the action of the Galois group on G(n,C2n) defined using ρ. We prove that the space of such embeddings are in bijective correspondence with the space of all holomorphic differential operators of order two on a rank n vector bundle over X with the property that the symbol of the operator is an isomorphism.

Item Type:Article
Source:Copyright of this article belongs to Elsevier Science.
Keywords:Differential Operator; Grassmann Embedding; Flat Connection
ID Code:3629
Deposited On:18 Oct 2010 10:18
Last Modified:18 Oct 2010 10:18

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